How is the centre of gravity calculated?

The CG is the total moment divided by the total weight. Each station's moment is its weight multiplied by its arm. Summing all moments and all weights, then dividing, gives the single arm at which the aircraft balances.

What is an arm and a moment?

The arm is the horizontal distance from the reference datum to a load, usually in inches. The moment is weight times arm, a measure of turning effect. Moments add up, which is why weight and balance works as a sum-and-divide problem.

What happens if the CG is out of limits?

An out-of-limits CG makes the aircraft unsafe to fly. Too far forward and it may be hard to flare or rotate; too far aft and it can become unstable or unrecoverable in a stall. The tool flags forward, aft, and overweight conditions.

Can I use this for any aircraft?

Yes, the method is universal. You supply the empty weight, empty arm, station arms, and the weight and CG limits from your specific aircraft's flight manual. The arithmetic is identical for a light single or a heavy jet.

Does it handle CG in percent MAC?

This tool reports CG as an arm in the same distance unit you enter, typically inches from datum. To convert to percent of mean aerodynamic chord, you would apply your aircraft's leading-edge-of-MAC arm and MAC length separately.

Aircraft Weight & Balance Calculator

Every flight starts with a weight and balance check, because an aircraft that is overweight or out of CG limits is dangerous regardless of how well it is flown. This calculator sums the weights and moments of every loading station, finds the loaded CG, and tells you immediately whether you are inside the envelope.

How it works

Each station contributes a weight and a moment, and the CG is the moment-weighted average position:

moment(station) = weight × arm
total weight = Σ weight
total moment = Σ moment
CG = total moment / total weight

The CG is then compared against the forward and aft limits, and the total weight against the maximum. The aircraft is legal to fly only when total weight is at or below the maximum and the CG lies between the forward and aft limits inclusive.

Example and notes

A light aircraft with a 1,400 lb empty weight at arm 39.0, 300 lb of fuel at 48.0, two 170 lb occupants at 37.0, and 50 lb of baggage at 95.0 has a total weight of 2,090 lb and a total moment of about 81,710 in-lb, giving a CG near 39.1 inches. If the flight manual allows up to 2,300 lb with CG limits of 35.0 to 47.3 inches, this loading is within both. Always recheck after any change to fuel or passengers, since burning fuel shifts the CG during the flight.